Amyloid-? (A?) is produced by the consecutive cleavage of
amyloid precursor protein (APP) first by ?-secretase,
generating C99, and then by ?-secretase. APP is also cleaved by
?-secretase. It is hypothesized that reducing the production of
A? in the brain may slow the progression of Alzheimer disease.
Therefore, different ?-secretase inhibitors have been developed
to reduce A? production. Paradoxically, it has been shown that
low to moderate inhibitor concentrations cause a rise in A?
production in different cell lines, in different animal models,
and also in humans. A mechanistic understanding of the A? rise
remains elusive. Here, a minimal mathematical model has been
developed that quantitatively describes the A? dynamics in cell
lines that exhibit the rise as well as in cell lines that do
not. The model includes steps of APP processing through both
the so-called amyloidogenic pathway and the so-called
non-amyloidogenic pathway. It is shown that the cross-talk
between these two pathways accounts for the increase in A?
production in response to inhibitor, i.e. an increase in C99
will inhibit the non-amyloidogenic pathway, redirecting APP to
be cleaved by ?-secretase, leading to an additional increase in
C99 that overcomes the loss in ?-secretase activity. With a
minor extension, the model also describes plasma A? profiles
observed in humans upon dosing with a ?-secretase inhibitor. In
conclusion, this mechanistic model rationalizes a series of
experimental results that spans from in vitro to in vivo and to
humans. This has important implications for the development of
drugs targeting A? production in Alzheimer disease.

To the extent possible under law, all copyright and related or
neighbouring rights to this encoded model have been dedicated to
the public domain worldwide. Please refer to
CC0
Public Domain Dedication for more information.

Quantitative modelling of the A? response across a range of inhibitor concentrations in two cell types (see below) from Figure 3 has been reproduced here. Percent of A? concentration after 16 hours along a range of inhibitor concentration (log scale -2 to 4) respect A? concentration when no drug treatment is applied.

Reactions for different conditions are found in Table 1 and 2 of the paper.
Secretase and inhibitor parameter values are found in Table S1a and S1b of the Supplementary section.

The simulation was done using Copasi v4.12 (Build 81) and the plots were generated using Gnuplot. Figure 3 is simulated by dividing the drug condition output by the no-drug condition output. The models with simulation settings can be downloaded from the below links:
- Copasi file of “Ortega2013 - Drug condition”
- Copasi file of “Ortega2013 – No-drug condition”